Solve for $x$ : $x^2 + x - 12 = 0$
Solution: The coefficient on the $x$ term is $1$ and the constant term is $-12$ , so we need to find two numbers that add up to $1$ and multiply to $-12$ The two numbers $-3$ and $4$ satisfy both conditions: $ {-3} + {4} = {1} $ $ {-3} \times {4} = {-12} $ $(x {-3}) (x + {4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -3) (x + 4) = 0$ $x - 3 = 0$ or $x + 4 = 0$ Thus, $x = 3$ and $x = -4$ are the solutions.